Enhancement of near-resonant degenerate four-wave-mixing signals by excitation of a coupled transition

Abstract

It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\ensuremath{\rightarrow}| b 〉$ transition which produces the DFWM signal is coupled to another transition ($ | a 〉\ensuremath{\rightarrow}| d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state $| b 〉$ and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth ${(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the inverse lifetime of the state $| b 〉$. The second effect derives from the effective lifetime acquired by the ground state $| a 〉$ due to its strong coupling to state $| d 〉$. This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth $\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}$, which is half the inverse lifetime of the state $| d 〉$. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.